In the present paper we derive the existence and uniqueness of a solution for the optimal control problem determined by a stochastic FitzHugh-Nagumo equation with recovery variable. In particular due the cubic non-linearity in the drift coefficients, standard techniques cannot be applied so that the Ekeland’s variational principle has to be exploited. AMS Classification subjects: 34K35, 35R60, ...

An application of the Exp-function method to search for exact solutions of nonlinear differential equations is analyzed. Typical mistakes of application of the Exp-function method are demonstrated. We show it is often required to simplify the exact solutions obtained. Possibilities of the Exp-function method and other approaches in mathematical physics are discussed. The application of the sing...

We develop a data-driven method, based on semi-supervised classification, to predict the asymptotic state of multistable systems when only sparse spatial measurements system are feasible. Our method predicts behavior an observed by quantifying its proximity states in precomputed library data. To quantify this proximity, we introduce sparsity-promoting metric-learning (SPML) optimization, which ...

Abstract We present a computer-assisted approach to prove the existence of Hopf bubbles and degenerate bifurcations in ordinary delay differential equations. apply method rigorously investigate these nonlocal orbit structures FitzHugh–Nagumo equation, extended Lorenz-84 model time-delay SI model.

Submitted: May 27, 2013; Accepted: Jul 5, 2013; Published: Jul 22, 2013 Abstract: In this paper, we present an algorithm called the Reduced Differential Transform Method (RDTM) to obtain approximate solutions for the Fitzhugh-Nagumo (FN) equation, Ito equation and find an exact solution to nonlinear PDE. The numerical results show that this method is a powerful tool for solving nonlinear PDEs a...

The FitzHugh-Nagumo equation provides a simple mathematical model of cardiac tissue as an excitable medium hosting spiral wave vortices. Here we present extensive numerical simulations studying long-term dynamics of knotted vortex string solutions for all torus knots up to crossing number 11. We demonstrate that FitzHugh-Nagumo evolution preserves the knot topology for all the examples presente...

A gradient particle method is used to compute probability densities for processes with delay bifurcations that are sensitive to very small noise. The method is particularly useful for computing the probability density in the transition region, where asymptotic approximations may not be valid. For a one dimensional steady bifurcation problem and a two-dimensional FitzHugh-Nagumo model we solve t...

Stochastic Resonance in a coupled FitzHugh-Nagumo equation is investigated. The optimal noise intensity and the optimal input frequency, which maximize the signal to noise ratio of the output signal, are studied numerically, and their dependence on system parameters and connection coe cients is examined. It is found that a network composed of six elements can separate a superimposed periodic pu...

In this article, we analyze traveling waves in a reaction–diffusionmechanics (RDM) system. The system consists of a modified FitzHugh–Nagumo equation, also known as the Aliev–Panfilov model, coupled bidirectionally with an elasticity equation for a deformable medium. In one direction, contraction and expansion of the elastic medium decreases and increases, respectively, the ionic currents and a...